In the common scheme of today's microcontrollers with the program code contained in on-board FLASH and data stored into on-board RAM I would suggest that a run time computed CRC table is a bad trade off on the use of RAM versus FLASH. I would really recommend that you use a pre-computed table and directly embed it into your code space so that the you do not "waste" RAM which is the more scarce resource on almost all MCUs.

If you are interested I have used a scheme that uses a table lookup scheme for CRC computation that uses a very small look up table of some 32-bytes by doing table look-up on data nibbles (4-bits at a time) instead of using a byte at a time scheme. The performance gain over bit serial methods is still substantial and with the speed of many modern MCSs the method is very usable in cases where a huge table is not attractive. The typical CRC table for byte-at-a-time schemes eats up 512 bytes.